Question

Check that the ratio  /G is dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify?

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Solution
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The given ratio is

Where,

Gravitational constant

Its unit is .

and  Masses of electron and proton.

Their unit is kg.

Electric charge.

Its unit is C.

constant

   

Permittivity of free space

Its unit is .

 Unit of the given ratio

                                                                       

Hence, the given ratio is dimensionless.

This is the ratio of electric force to the gravitational force between a proton and an electron, keeping distance between them constant.

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